Capillaries are commonly found on small systems

The capillary tube is the simplest type of expansion device you could use.

Essentially,
it is a very small bore tube that is selected such that the frictional pressure
drop equals the required pressure drop between the condensing and evaporating
pressures.

Since there are already some fittings in the liquid line and at the
evaporator there is a distributor, tails and the evaporator itself, these
pressure drops must be included.

Going from 3 to 4 is complicated by the change in
refrigerant quality. We solve the problem by a step-by-step simulation
where at each step, the incremental length to achieve a temperature difference
of 1°C is calculated.

At each step, the following equations are solved:

Mass conservation

Energy conservation

Momentum conservation

At
the end of the simulation, the incremental lengths are summed to give the total
capillary length. Of course, this is just an estimate since it is based on
theory only but it does give a good starting guess. The final selection is
by cut and try.

An interesting feature of the calculation is the emergence of the choked flow
concept. As you reduce the suction pressure, you will eventually reach a
point when a further increase in mass flow is impossible. This appears as
a negative incremental length, clearly an impossible situation. If this
occurs, we terminate the calculation and report the suction temperature when the
calculation was stopped. The best way out of this is to increase the tube
diameter. The idea is to find the smallest possible tube without getting
choked flow. This would result in the shortest tube length.